Solar Panel - Event Date: 12 Feb 2020

80 amp hours of LI battery is good for most folks.  It should provide enough current to run the microwave but you would need to buy a 2KW or larger sine wave inverter. Like this for example:

It will draw something like 150 amps from the battery running the micro so you will want to locate the inverter as close to the battery as possible and run at least 1/0 gauge wire to it from the battery, which is big stuff. 

If the charge controller that came with your solar modules is not set up for Li battery charging you should consider very carefully before you use it. Again, lithium batteries can catch fire if overcharged. Proper wire sizing and fuse protection for all the system components is also critical for safety. 

Documentation? There are numerous online resources. For lithium batteries and batteries in general I would take a look at batteryuniversity.com.  That's probably a good place to start. 

Are the two 40AH batteries you got 12V or 6V?  If they are 12V then you will be connecting them in parallel and will have 80AH capacity. if 6V then they need to be connected in series so you will have 40AH capacity. 

40AH is small for most folks, even though you can use most of that capacity with Li batteries. You should still not use more than than about 80-85% if you want to get long life out of them. So that's about 35AH in practice. 

All Li batteries are "smart" in that they need a battery management system (BMS) to be operated safely. So, be careful to really understand what protections the BMS your batteries have provides. If you overcharge Li batteries they can catch fire. The WFCO charger in your rPod left to its own can overcharge them. WFCO and others make different chargers meant for use with Li batteries. 

The other consideration besides overcharging is excessive discharging. Lead acid batteries can run as high as 14.4 V charging and as low as 11-11.5 V discharging. Li batteries have a much narrower voltage range, so if you have a Li battery that charges up to 14V it will be fully discharged around 12.5-13V. In other words, you don't want to discharge a Li battery to as low a voltage as you would a lead acid one. A battery monitor will help you to track your battery state of charge. They are available pretty inexpensively these days. 

Re inverters, no you don't really need one. You can't run your a/c on battery anyway, it takes waaay to much energy. That leaves your microwave and TV as the ac loads in the trailer as it comes from the factory. You can get a dual voltage TV pretty inexpensively, so that can be run efficiently on 12V. The microwave can in theory be run for short periods (a few minutes at most) from an inverter, but you'd need at least a 2kw inverter for that and a 40AH battery probably can't produce enough current to run it. So if you do without your microwave while boondocking you won't need an inverter unless you add some other ac loads to the trailer.     

No schematic but as GlueGuy says the circuits are pretty simple. Assuming by "two harnesses" you mean the 4 wires connected to the tongue mounted battery, one pair of these should go to the solar connector on the side of the trailer, the other pair (the ones with voltage on them) to the ac charger and dc fuse panel. 

You do not need to use the existing wires going to the solar connector. Many folks find it more convenient to run their own conductors from their batteries to their charge controller and on to their solar modules. Either way, please DO install a fuse or circuit breaker at the battery, it is unsafe to run an unprotected circuit from the battery, if you get a short you can burn up your trailer. 

Use at least 10 gauge wire and a 30A fuse. If you plan to keep your solar modules portable and run a longer set of conductors to them (over about 20 feet one way) then go to 8 gauge wire to keep your voltage losses down. 

You will need a solar charge controller configured for lithium batteries and should change out your ac charger as well, lithium batteries need a different charge protocol than lead acid batts. Also, you should not attempt to charge lithium batteries when they are below freezing, so many folks relocate them to the inside of their trailers from the tongue so they stay warm. 

When you say you want to extend beyond the 40 amp capacity of the batteries you have, I think you probably mean 40 amp hours. Amp hours are a measure of battery capacity. Amps are a measure of instantaneous power from the battery (assuming a nominal 12V battery).

 If you add 200 watts of solar to your system that will produce around 12-13 amps at full sun as GlueGuy says. Over a typical 4-5 hours full sun on a decent day you would get around 50 amp hours, more than what your battery can take even if you start with it fully discharged. What I'm leading up to is that 200 watts is really too much for a 40 amp hour battery. I would suggest staying with about 100 watts of solar and consider getting more battery capacity first before adding more solar (assuming you need more).